How can I get a list of approved quotes that have not yet been converted into a project?

I think you can do this by defining a view that filters on the quote status "Approved by client". Also make sure to give the view the column 'Total Agreed'. In the Dashboard, you can then create a widget of type 'Total Sum', set scope to Quote, select the newly created view and choose the column Total Agreed for the sum..

Thanks Lennart! The problem with this solution is that it shows ALL quotes that have been approved, but I'm looking for those that have been approved, but not yet converted into a project.

I think what Lennart said was correct, those that have already been converted to projects have the status "Approved", the others which are still only in the quote phase have the status "Approved by client".

Yes! You are right of course! I was convinced Approved by Client was when a client approved a quote, and Approved when its status was changed by a PM in the HP instead of by the client. But this isn't even possible without converting into a project so my point is moot. 

Thanks for getting me out of my delusions, even if it took a while :-D